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Mayara Longo Vivian, a leader of the Free Fare Movement, said there had been "concrete measures" among the president's proposals and that the "fight would continue".

Analysis

By Gary DuffyExecutive editor, BBC Brasil, Sao Paulo

The most headline-catching part of her proposals was to suggest a referendum to establish a constitutional assembly to consider political reform. It has the advantage of handing a decision back to the people, but is also a commitment to what will be a long drawn out process that will allow the government time to draw breath.

It is either a bold move or a very clever one.

Some are already arguing it could be unconstitutional - others are complaining that political reform didn't need such an elaborate proposal and could have been done more effectively and with greater speed. In a country plagued by dodgy deals few are going to argue with the idea of making corruption a more serious offence. However Brazilians are more likely to be impressed when the corrupt are actually convicted and jailed.

On Monday evening, there were fresh demonstrations in several cities, although they appeared to be smaller than those that led to clashes with police last week.

The BBC's Julia Carneiro in Rio de Janeiro says exactly a week ago 100,000 people marched down the city's Rio Branco Avenue, but on Monday just a few dozen were chanting in front of the Candelaria church.

More people joined in as they marched, and soon a few thousand demonstrators had popped up and were occupying the city centre's main avenue.

Street vendors were selling Brazilian flags and Anonymous masks for those who came unprepared, she says.

In other protests, hundreds of people blocked the main road to Brazil's busiest port, Santos, and hundreds more came out to protest against corruption in the capital, Brasilia.

Two women were killed at a protest in the central state of Goias, not far from Brasilia. Police said they were killed by a driver who sped through a roadblock they had set up with other protesters.

The deaths bring to four the total number of lives lost in the unrest.

'Signals'

The president met leaders of one protest faction before meeting with state governors and mayors.

Image caption
The protests have become the largest of their kind in Brazil in at least two decades

"My government is listening to democratic voices," she told a televised news conference.

"We must learn to hear the voices of the street. We all must, without exception, understand these signals with humility and accuracy.

"Brazil is ready to move forward and has made it clear it does not want to stand where it is."

She also suggested tougher penalties for corruption, and warned against any repeat of the violence that was seen last Thursday.

'No plan B'

Ms Rousseff faces re-election next year, when Brazil is also due to host the football World Cup. Rio de Janeiro will also host the Olympics in 2016.

Many of those demonstrating are unhappy at the cost of building stadiums in a country where many live in poverty and ticket prices for such prestigious international competitions are out of reach.

Brazilian press on proposals

The former president of the Supreme Court, Carlos Velloso, says the proposals are "a way of distracting the people who are [protesting] in the streets", according to O Estado de Sao Paulo newspaper. Mr Velloso says that the protesters are demanding an "end to unbridled spending and a reform which will improve the political regime".

Sao Paulo daily Folha writes that opposition lawmakers accuse the president of "going over Congress' head". "It is one of Congress' exclusive competencies to call a referendum," the paper quotes Senator Aecio Neves as saying.

Unrest has dogged many of the fixtures currently taking place in Brazil as part of Fifa's Confederations Cup, seen as a dress rehearsal for the World Cup and using many of the same facilities.

Fifa's Secretary General Jerome Valcke has said the organisation has "no plan B" for next year's World Cup.

The wave of rallies in more than 100 cities began in Sao Paulo, where residents were unhappy at planned rises in public-transport fares.

Those increases have since been shelved, but the protests rapidly became more widespread and the protesters' demands more wide-ranging.

Brazilians have been demanding better health and education, saying they are fed up with paying relatively high taxes and feel that they do not get enough back from the state.

Protesters are also angry about corruption and are scornful of politicians.